Conway's Game of Life

A cellular automaton that demonstrates how complex patterns can emerge from simple rules. Click cells to bring them to life, then watch evolution unfold.

About the Game of Life

The Game of Life is a cellular automaton devised by mathematician John Conway in 1970. It's a zero-player game, meaning its evolution is determined by its initial state, requiring no further input.

What makes this cellular automaton truly fascinating is its computational universality. Despite having only four simple rules, the Game of Life is Turing complete, meaning it can simulate any computation that can be performed by a computer. In fact, it's theoretically possible to build the entire Game of Life within itself – creating a recursive, self-contained universe where patterns can compute, store information, and even replicate themselves.

I first discovered this mesmerizing world through ScienceEtonnante's excellent video which beautifully explains the mathematical foundations. Later, I watched an Arte documentary that delved into Conway's life and mathematical legacy, and finally discovered Ego's visual exploration of the stunning patterns that emerge from these simple rules.

The Rules

  1. Any live cell with fewer than two live neighbors dies (underpopulation)
  2. Any live cell with more than three live neighbors dies (overpopulation)
  3. Any live cell with two or three live neighbors lives on to the next generation
  4. Any dead cell with exactly three live neighbors becomes a live cell (reproduction)

Common Patterns

Over the decades, enthusiasts have discovered and catalogued thousands of patterns. Here are some of the most fundamental ones:

Still Lifes

Block - remains unchanged

Blinker

Oscillates every 2 generations

Glider

Moves diagonally across the grid

Beacon

Oscillates every 2 generations

Toad

Oscillates every 2 generations

Pulsar

Complex oscillator (period 3)

These are just a few examples of the thousands of patterns discovered over the decades. Each pattern tells a story of emergence, complexity, and mathematical beauty.

Wikipedia: Examples of Patterns — Comprehensive catalog with detailed descriptions

Conway Life Pattern Library — Interactive collection of patterns to explore

Further Reading

Wikipedia: Conway's Game of Life — Comprehensive overview and mathematical details

LifeWiki — Extensive catalog of patterns and discoveries

Play Game of Life — Interactive simulator with preset patterns